I have done quests for lord and ladies. A couple of times they gave me some mercenaries who they didnt want anymore but couldnt get rid of. I then had to sell them to another lord or lady using the 'convince'system. I just think its very rare to come across and they havent added more quests with them.
I have run across this quest once or twice and it worked but first of all it is very rare, and speaking of reputation I do not only mean quests, but all the actions, that should have a positive impact, but have none at all instead,
For example:
-Aiding lords in battle
-Giving gifts
-Destroying bandit hideouts ( With this one it even says that the destruction supposedly increases your relations with nearby notables by 2, but I have never noted any change at all.
-Attacking the enemy of your faction
I even gave the Dragon Banner to a king, he told me how much he is grateful and so on, but relations remained unchanged.
I am sure that one could find more examples, but this is enough to just outline the issue.
In my main playthrough I also came acoss an issue, where the game treats mercenary contract as a vassalage, therefore after breaking it I got -20 relation points with everyone who was in the faction at that time, making it actually impossible to fix this situation.